We propose to continue work on the use of computationally intensive methods to fine-map genes involved in complex traits. This work was previously supported under our grant "'Computational methods in genetic epidemiology" (GM58897, PI: D. Thomas). The present incarnation is a more focused version of this earlier grant. Our particular emphasis is on methods that exploit the underlying genealogy (ancestry) of a sample of interest. The pattern of haplotype diversity, D, one sees in a sample of individuals is the result of a complex interaction between the unobserved genealogy, G, of the sample (which itself is a function of recombination) and the forces of mutation acting upon that genealogy. This is further influenced by the shared ancestry induced by the presence of the functional mutation(s) related to the trait of interest. This results in linkage disequilibrium in regions close to functional mutations. In principle, one wishes to explore the space of possible genealogies that might give rise to a particular data set and use this as a basis for an approach to mapping. Such an approach is likely to be impossible, or prohibitively expensive computationally. We therefore propose to adopt the following two approximations to this desired goal: - Genealogical methods in which we explicitly include the unobserved genealogy of the sample of interest, but use hybrid rejection/MCMC methods to avoid calculating P (DIG), (this quantity can only be calculated for a family of simplistic, unrealistic mutation models). - Bayes methods, which abstract out the effects of the genealogy using hierarchical clustering techniques.